I'll try to get you started.

The ordinary power series generating function for the value of an even number of nickels,at most 20, is

for an odd number of dimes, at most 12 (i.e., at most 11)

for at least 2 quarters,

Multiply those three series together and you have the generating function for the number of ways to make change using the specified coins. You will have to sum the series involved in order to get your answer in the form of a rational function.